Geometric Attitude Tracking Control for Rigid Body Based on a Novel Attitude Error Dynamic Model on SO(3)

This paper provides some new results for attitude tracking control for rigid body. In order to avoid the complexity and ambiguity associated with other attitude representations (such as Euler angles or quaternions), the attitude dynamics and the proposed control system are represented globally on special orthogonal groups. Based on a special attitude error, we construct a novel attitude error dynamic model, and develop a baseline controller which ensures the asymptotic attitude tracking almost globally in the absence of disturbances and uncertainties. To account for external disturbances and parametric uncertainties, adaptive laws are introduced to estimate the unknown bound of the equivalent disturbance as well as the inertia matrix of the rigid body. Then, an almost global adaptive attitude tracking controller is developed to track a given desired attitude trajectory without requiring the exact knowledge of inertia matrix, while guaranteeing boundedness of tracking errors. Finally, both simulation and experimental results are presented to demonstrate the efficiency of the proposed controllers.